UCLA

Optimal transport theory provides a distance between two probability distributions. It finds the cheapest transport map that moves one measure to the other measure for some ground cost. With its deep theoretical properties, the optimal transport distance has been used in diverse areas such as partial differential equations (PDEs), economics, image processing, and machine learning. However, computing the optimal transport distances and maps is difficult, which has been a significant challenge in applications. In this dissertation, we present new numerical methods using optimal transport distance and their applications in solving challenging convex and nonconvex optimization problems involving non-linear PDEs. We demonstrate the suggested methods’ efficiency through numerous numerical results.